Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
91
A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
Answer:
13 days
A's efficiency = 1.3 B. A takes 23 days, so total work = 1.3B * 23 = 29.9B. Together their efficiency is A+B = 1.3B + B = 2.3B. Time = 29.9B / 2.3B = 13 days.
92
A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B, and C together can finish it in 6 days. A and C together will do it in:
Answer:
8 days
A+B+C = 1/6. A+B = 1/8 => C = 1/6 - 1/8 = 1/24. B+C = 1/12 => A = 1/6 - 1/12 = 1/12. A+C = 1/12 + 1/24 = 3/24 = 1/8. They take 8 days.
93
A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in:
Answer:
12 days
A+B rate = 1/15 + 1/10 = 5/30 = 1/6. 2 days work = 2/6 = 1/3. Remaining 2/3 done by A. A takes (2/3)*15 = 10 days. Total days = 2 + 10 = 12 days.
94
A takes 3 times as long as B and C together to do a job. B takes 4 times as long as A and C together. If all 3 take 24 days, how long does A take?
Answer:
96 days
A = 3(B+C) means A does 1/4 of total work. Total takes 24 days. A takes 24 * 4 = 96 days.
95
A and B can do a work in 10 and 15 days respectively. A starts the work and they work on alternate days. The work will be finished in:
Answer:
12 days
Cycle of 2 days = 1/10 + 1/15 = 1/6. Total cycles = 6. Total time = 6 * 2 = 12 days.
96
Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both worked together. B working alone takes 4.5 hours more than if both worked together. Time taken by them together?
Answer:
6 hours
Let time taken together be x. A takes x+8, B takes x+4.5. The formula is x = sqrt(a * b) where a and b are the extra times. x = sqrt(8 * 4.5) = sqrt(36) = 6 hours.
97
A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
Answer:
60 days
A works 16 days, B works 44 days. This is equal to (A+B) working for 16 days, and B working for 28 days alone. (A+B) does 16/30 = 8/15 work. Remaining 7/15 is done by B in 28 days. B's full time = 28 * (15/7) = 60 days.
98
If 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days, in how many days will 10 women complete it?
Answer:
40 days
8(4M+6W) = 10(3M+7W) => 32M+48W = 30M+70W => 2M = 22W => M = 11W. Work = 8(4(11W)+6W) = 8(50W) = 400W-days. 10 women will take 400 / 10 = 40 days.
99
A can finish a work in 20 days. He worked for 10 days, and the remaining work was finished by B in 15 days. B alone can finish the whole work in:
Answer:
30 days
A does 10/20 = 1/2 of the work. B does 1/2 of the work in 15 days. B alone would take 15 * 2 = 30 days.
100
Pipe A fills a tank in 2 hours and Pipe B fills it in 3 hours. Pipe C can empty it in 6 hours. If all three are opened, how long to fill the tank?
Answer:
1.5 hours
Rate = 1/2 + 1/3 - 1/6 = 3/6 + 2/6 - 1/6 = 4/6 = 2/3. Time = 3/2 = 1.5 hours.